Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

if A is a $2 \times 2$ matrix with t r A = 5 and det A = - 14 what are the eigenvalues of A?

The eigenvalues of A.

$A = [\begin{matrix} a & b \\ c & d \end{matrix}], t r A = 5 λ^{2} - 5 λ - 14 = 0 (λ + 2) (λ - 7) = 0 λ_{1} = 2, λ_{2} = 7$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: definition of matrix

A function is defined as a relationship between a set of inputs that each have one output.

$A = [\begin{matrix} a & b \\ c & d \end{matrix}], tr A = 5$

Now,

we solve: A = - 14

$\det (a - λl) = 0 |\begin{matrix} a - λ & b \\ c & d - λ = 0 \end{matrix}|$

Step 2: definition of eigenvalues

The eigenvalue is a number that indicates how much variance exists in the data in that direction; in the example above, the eigenvalue is a number that indicates how spread out the data is on the line.

Multiply the matrix:

$(a - λ) (d - λ) - bc = 0 λ^{2} - (a + d) λ + ad - bc = 0 λ^{2} - 5 λ - 14 = 0 (1 - λ) (2 - λ) = 0$

_So,

$λ_{1} = - 2, λ_{2} = 7$

Hence, $λ_{1} = - 2, λ_{2} = 7$

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Linear Algebra With Applications

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Short Answer

if A is a $2 \times 2$ matrix with t r A = 5 and det A = - 14 what are the eigenvalues of A?

Step by Step Solution

Step 1: definition of matrix

Step 2: definition of eigenvalues

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Linear Algebra With Applications

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Short Answer

if A is a 2×2matrix with t r A = 5 and det A = - 14 what are the eigenvalues of A?

Step by Step Solution

Step 1: definition of matrix

Step 2: definition of eigenvalues

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if A is a $2 \times 2$ matrix with t r A = 5 and det A = - 14 what are the eigenvalues of A?